Conclusion The constraint of affine covariance has been shown in this part to be relevant for the derivation of time-frequency representations. It leads to a class of affine distributions which is the counterpart of the Cohen's class associated to time and frequency translations. These two classes can also be seen as a result of some 2D correlation acting on the WVD. We have thereby derived a large class of time-scale and time-frequency representations, on which many possible (and sometimes exclusive) properties may be imposed. We have studied several specific requirements (such as energy normalization, time marginals ...) and associated parameterization of the representation. There is obviously a great versatility for the choice of representations, which may be appropriate for various applications. Each one is appropriate to describe properly specific characteristics of a signal, and one has to benefit from the complementarity of these tools. Vice versa, a good interpretation of the time-frequency and time-scale images necessitates a deep knowledge of the mechanisms of information's allocation in the plane.
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